Realisation and dismantlability

Sebastian Hensel; Damian Osajda; Piotr Przytycki

doi:10.2140/gt.2014.18.2079

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arXiv · 1205.0513

Realisation and dismantlability

Sebastian Hensel·Damian Osajda·Piotr Przytycki

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Abstract

We study dismantling properties of the arc, disc and sphere graphs. We prove that any finite subgroup H of the mapping class group of a surface with punctures, the handlebody group, or Out(F_n) fixes a filling (resp. simple) clique in the appropriate graph. We deduce realisation theorems, in particular the Nielsen Realisation Problem in the case of a nonempty set of punctures. We also prove that infinite H have either empty or contractible fixed point sets in the corresponding complexes. Furthermore, we show that their spines are classifying spaces for proper actions for mapping class groups and Out(F_n).

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BibTeX RIS

Sebastian Hensel, Damian Osajda, Piotr Przytycki. 2012-05-02. Realisation and dismantlability. https://doi.org/10.2140/gt.2014.18.2079

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